1/* notes.pl 2Author: Gimenez, Christian. 3 4Copyright (C) 2025 Gimenez, Christian 5 6This program is free software: you can redistribute it and/or modify 7it under the terms of the GNU General Public License as published by 8the Free Software Foundation, either version 3 of the License, or 9at your option) any later version. 10 11This program is distributed in the hope that it will be useful, 12but WITHOUT ANY WARRANTY; without even the implied warranty of 13MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 14GNU General Public License for more details. 15 16You should have received a copy of the GNU General Public License 17along with this program. If not, see <http://www.gnu.org/licenses/>. 18 192025-10-12 20*/ 21 22:- module(notes, [ 23 note_order/1, 24 notenum/2, 25 sum_semitones/3, 26 sum_tones/3, 27 tone/2, 28 semitone/2, 29 semitones/3, 30 interval/2, 31 interval/3, 32 second/3, 33 third/3, 34 fourth/2, 35 fifth/2, 36 sixth/3, 37 seventh/3, 38 eighth/2, 39 octave/2, 40 transpose/3, 41 transpose/4 42 ]).
93:- license(gplv3).
98note_order([c, cs, d, ds, e, f, fs, g, gs, a, as, b]).notenum(c, R) will result in R = 0, and without more results.
But notenum(c, 12) is also true (indicating that C note is also represented
as 12).
Representing notes in numbers are easy for calculations. Adding an amount of semitones to a given note represented as a number instead as a Prolog atom is more efficient.
If Num is a negative number or greater than 11, it is calculated to be between 0 (c note) to 11 (b note).
115notenum(c, 0) :- !. 116notenum(cs, 1) :- !. 117notenum(d, 2) :- !. 118notenum(ds, 3) :- !. 119notenum(e, 4) :- !. 120notenum(f, 5) :- !. 121notenum(fs, 6) :- !. 122notenum(g, 7) :- !. 123notenum(gs, 8) :- !. 124notenum(a, 9) :- !. 125notenum(as, 10) :- !. 126notenum(b, 11) :- !. 127notenum(Note, Num) :- 128 % Case: Num is not between 0 and 11 semitones. 129 (Num > 11 ; Num < 0), !, 130 131 ResultNum is Num mod 12, 132 notenum(Note, ResultNum).
141sum_semitones(Note-Octave, Semitones, ResultNote-ResultOctave) :- !, 142 notenum(Note, Num), 143 ResultNum is Num + Semitones, 144 notenum(ResultNote, ResultNum), 145 146 Diff is (ResultNum div 12), 147 148 ResultOctave is Octave + Diff. 149sum_semitones(Note, Semitones, ResultNote) :- 150 atom(Note), 151 notenum(Note, Num), 152 ResultNum is Num + Semitones, 153 notenum(ResultNote, ResultNum).
161sum_tones(Note, Tones, ResultNote) :-
162 Semitones is Tones * 2,
163 sum_semitones(Note, Semitones, ResultNote).
171tone(Note, ResultNote) :-
172 sum_semitones(Note, 2, ResultNote).
180semitone(Note, ResultNote) :-
181 sum_semitones(Note, 1, ResultNote).191semitones(FromNote-FromOctave, ToNote-ToOctave, Diff) :- !, 192 semitones(FromNote, ToNote, Diff1), 193 Diff is Diff1 + (ToOctave - FromOctave) * 12. 194semitones(FromNote, ToNote, Diff) :- 195 notenum(FromNote, Num), 196 notenum(ToNote, Num2), 197 Diff is Num2 - Num.
In the literature, the interval between 4-perfect and 5-perfect (6 semitones) has no name. In this implementation, the term 4-extra is assigned to this interval.
210interval(1-perfect, 0) :- !. 211interval(2-minor, 1) :- !. 212interval(2-major, 2) :- !. 213interval(3-minor, 3) :- !. 214interval(3-major, 4) :- !. 215interval(4-perfect, 5) :- !. 216interval(4-extra, 6) :- !. % 6 semitones interval has no name actually. 217interval(5-perfect, 7) :- !. 218interval(6-minor, 8) :- !. 219interval(6-major, 9) :- !. 220interval(7-minor, 10) :- !. 221interval(7-major, 11) :- !. 222interval(Num-Type, Semitones) :- 223 (Num > 7 ; Num < 1), !, 224 225 Octave is Num div 8, 226 Num2 is Num mod 7, 227 interval(Num2-Type, Semitones1), 228 229 Semitones is (Octave * 11) + Semitones1 + 1.
234interval(Interval, StartNote, EndNote) :-
235 interval(Interval, Semitones),
236 sum_semitones(StartNote, Semitones, EndNote).
243second(Type, A, B) :-
244 interval(2-Type, Semitones),
245 sum_semitones(A, Semitones, B).
252third(Type, A, B) :-
253 interval(3-Type, Semitones),
254 sum_semitones(A, Semitones, B).
259fourth(A, B) :-
260 sum_semitones(A, 5, B).
265fifth(A, B) :-
266 sum_semitones(A, 7, B).
273sixth(Type, A, B) :-
274 interval(6-Type, Semitones),
275 sum_semitones(A, Semitones, B).
282seventh(Type, A, B) :-
283 interval(7-Type, Semitones),
284 sum_semitones(A, Semitones, B).Same as octave/2.
291eighth(A, B) :-
292 sum_semitones(A, 12, B).Same as eighth/2.
299octave(A, B) :- 300 sum_semitones(A, 12, B). 301 302sum_semitones_int(Semitones, Note, Note2) :- 303 sum_semitones(Note, Semitones, Note2).
308transpose(Notes, Semitones, NewNotes) :-
309 maplist(sum_semitones_int(Semitones), Notes, NewNotes).
320transpose(Notes, FromNote, ToNote, NewNotes) :-
321 semitones(FromNote, ToNote, Diff),
322
323 transpose(Notes, Diff, NewNotes)
notes: Simple notes representation and calculation.
Predicates that calculates semitones, tones, and intervals in notes.
Names
In order to create a more convenient way to programming with Prolog, name of notes, intervals, and othe possible concepts are different from literature. It may be different from Lilypond or other software too.
For instance, C3 is not used to represent C note in Prolog in third octave because the it would be interpreted as a Prolog variable. Also,
'C3'orc3wolud requier extra processing to separate the octave number from the C/c. However, thec-3term would represent the C note at 3 octave effectively, and the octave number is already separated from the note name. A simmilar approach is implemented for intervals and other concepts.Note representation
Notes are terms with the following possible representations:
c(C note),ds(D# or D sharp), etc.Note-Octave. For example:c-2(C2 note),ds-2(D#2 or D2 sharp), etc.Only sharp notation is used to represent the notes in Prolog (as in
csfor C sharp). No bemol are used in this implementation (ebis not considered as E bemol, insteaddsshould be used to represent the same note).Intervals
Interval calculations can be achieved by the interval/2 and interval/3 predicates, or by using sum_semitones/3 with the specific amount of semitones. There are also aliases for second/3, third/3, etc.
Intervals are represented as:
Nth-Type. Where Nth is the number of interval, and the Type is one of the atoms:perfect,major,minor, orextra. The4-extraatom is used to assign a name to the interval between the P4 (perfect 4th) and P5 (perfect 5th) which has 6 semitones of distance. This interval name does not exists in the literature, and is used to complete the names to a semitone distance in case the calculations results in that number.